Question

David Palmer identified the following bonds for investment: 1) Bond A: A $1 million par, 10% annual coupon bond, which will mature on July 1, 2025. 2) Bond B: A $1 million par, 14% semi-annual coupon bond (interest will be paid on January 1 and July 1 each year), which will mature on July 1, 2031. 3) Bond C: A $1 million par, 10% quarterly coupon bond (interest will be paid on January 1, April 1, July 1, and October 1 each year), which will mature on July 1, 2026. The three bonds were issued on July 1, 2011. (Each Part is Independent)

(a) If Bond B is issued at face value and both Bond B and Bond A are having the same yield to maturity (EAR), calculate the market price of Bond A on July 1, 2011. [Note: Full mark would only be given to correct answer of which the values of those variables not provided in the question directly are derived.]

(b) David purchased the Bond C on January 1, 2014 when Bond C was priced to have a yield to maturity (EAR) of 10.3812891%. David subsequently sold Bond C on January 1, 2016 when it was priced to have a yield to maturity (EAR) of 12.550881%. Assume all interests received were reinvested to earn a rate of return of 3% per quarter (from another investment account), calculate the current yield, capital gain yield and the 2-year total rate of return (HPY) on investment for David on January 1, 2016. [Hint: Be careful with how many rounds of coupons has David received during the holding period and thus how much interests (coupons and reinvestment of coupons) he has earned in total during the 2-year holding period.]

(c) David purchased Bond B on a coupon payment day. Bond B is priced to have a yield to maturity (EAR) of 12.36% and its market value is $1,101,058.953 on the date of purchase. Find the remaining life until maturity (in terms of 6-month period or year) of Bond B.

Answer 1

(a) 1,262,364.04

Bond Price of Bond B = Face Value of Bond B = $1,000,000

Yield to Maturity for Bond B = 7% [14% / 2]

YTM of Bond B = YTM of Bond A

Bond Price of Bond A ​= Coupon  × (1 −(1/(1+YTM)ⁿ​)​) + Face Value  × (1 / (1+YTM)ⁿ)​

Bond Price of Bond A = ($1,000,000 x 10%) x (1 - (1/(1+7%)¹⁴)) + ($1,000,000 x (1 / (1+7%)¹⁴))

Bond Price of Bond A = $1,262,364.04

(b) Current Yield = 12.21%

Bond Price of Bond C on Purchase = ($1,000,000 x 2.5%) x (1 - (1/(1+10.3812891%)⁵⁰)) + ($1,000,000 x (1 / (1+10.3812891%)⁵⁰))

Bond Price of Bond C on Purchase = $246,258 (January 2014)

Bond Price of Bond C on Sale = ($1,000,000 x 2.5%) x (1 - (1/(1+12.550881%)⁴²)) + ($1,000,000 x (1 / (1+12.550881%)⁴²))

Bond Price of Bond C on Sale = $204,772 (January 2016)

Current Yield = Coupon / Price

Current Yield = $25,000 / $204,772

Current Yield = 12.21%

Capital Gains Yield = 16.85%

Capital Gains Yield = (Bond Price on Purchase - Bond Price on Sale) / (Bond Price on Purchase)

Capital Gains Yield = ($246,258 - $204,772) / $246,258

Return on investment = 14%

Period	Coupon	Reinv. Amt	Rate	Interest	Total
01-Apr-14	25000	25,000	3%	750	25,750
01-Jul-14	25000	50,750	3%	1,523	52,273
01-Oct-14	25000	77,273	3%	2,318	79,591
01-Jan-15	25000	1,04,591	3%	3,138	1,07,728
01-Apr-15	25000	1,32,728	3%	3,982	1,36,710
01-Jul-15	25000	1,61,710	3%	4,851	1,66,562
01-Oct-15	25000	1,91,562	3%	5,747	1,97,308
01-Jan-16	25000	2,22,308	3%	6,669	2,28,978
	200000			Rate of Return	14%